The only canon characters I can think of who are effectively immoral are the Denarians ... not because they are immortal themselves, Highlander style, but because they play host to an immortal being. In the case of the Denarians, it's a fallen angel.
I would say that your character could become immortal through any of a few different means that have been featured in stories. Unfortunately most of the ones I know off aren't very nice ways to become immortal *grins*
A mystic artifact is always a good choice, but then what happens if they lose it?
Partnership with an immortal being is another option. I ran a character in a Buffy game, a small time thief who stole a sword that a demon had been bound into. Unfortunately the demon, having been held in a buddhist monastary for centuries had gone a little loopy, decided it wanted to be buddhist iself, and had rededicated itself to fighting monsters and evil. My character had the choice of going along with this, or fighting ... and that usually meant he'd end up losing control of his own body, being possessed, and fighting the evil anyway. Unfortunately he couldn't get rid of the sword and demon, so was stuck with the situation.
There's a mercenary character who I think has some kind of supernatural power link as well, but I can't recall if its ever been nailed down exactly what.
Now, if your character is coming from Ancient Egypt, maybe she has some kind of link to the Gods from then.
Another option is rather than living one life, she continues to die and be reborn. Her spirit moves into a new body, taking over that identity, but keeping her own memories. If the body she moves into has suffered some great trauma / near death experience / been clinically dead for a time, then that might explain how the personality would change afterwards. That way it might be the result of a curse she is suffering from.
Do any of those ideas interest you?